{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:L6DRFMR54IZ2ULJZJLEAMKZHOX","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"afc4d45b8521e5db9df8367c839c49e31c9668a30fe6ab44805d0ebf9df92ee9","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2014-07-27T08:45:48Z","title_canon_sha256":"eab16a68c2cd246a55fc00df1d24b13a0d53d664d50676e0d459be32d0585ca4"},"schema_version":"1.0","source":{"id":"1407.7201","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.7201","created_at":"2026-05-18T01:00:46Z"},{"alias_kind":"arxiv_version","alias_value":"1407.7201v4","created_at":"2026-05-18T01:00:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.7201","created_at":"2026-05-18T01:00:46Z"},{"alias_kind":"pith_short_12","alias_value":"L6DRFMR54IZ2","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"L6DRFMR54IZ2ULJZ","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"L6DRFMR5","created_at":"2026-05-18T12:28:35Z"}],"graph_snapshots":[{"event_id":"sha256:972d9200fd62beae7c6ac26ad800f012688246f657a85379394c47580361b1b3","target":"graph","created_at":"2026-05-18T01:00:46Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We record various properties of twisted Becker-Gottlieb transfer maps and study their multiplicative properties analogous to Becker-Gottlieb transfer. We show these twisted transfer maps factorise through Becker-Schultz-Mann-Miller-Miller transfer; some of these might be well known. We apply this to show that $BSO(2n+1)_+$ splits off $MTO(2n)$, which after localisation away from $2$, refines to a homotopy equivalence $MTO(2n)\\simeq BO(2n)_+$ as well as $MTO(2n+1)\\simeq *$ for all $n\\geqslant0$. This reduces the study of $MTO(n)$ to the $2$-localised case. At the prime $2$ our splitting allows ","authors_text":"Hadi Zare, Takuji Kashiwabara","cross_cats":["math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2014-07-27T08:45:48Z","title":"Splitting Madsen-Tillmann spectra I. Twisted transfer maps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.7201","kind":"arxiv","version":4},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:e4b243e9ec190d4c8116a8424fca9cf4e0f4096914bbb9b2028917b4224376ea","target":"record","created_at":"2026-05-18T01:00:46Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"afc4d45b8521e5db9df8367c839c49e31c9668a30fe6ab44805d0ebf9df92ee9","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2014-07-27T08:45:48Z","title_canon_sha256":"eab16a68c2cd246a55fc00df1d24b13a0d53d664d50676e0d459be32d0585ca4"},"schema_version":"1.0","source":{"id":"1407.7201","kind":"arxiv","version":4}},"canonical_sha256":"5f8712b23de233aa2d394ac8062b2775fc8498f3489faeed392ac3ecdc482548","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5f8712b23de233aa2d394ac8062b2775fc8498f3489faeed392ac3ecdc482548","first_computed_at":"2026-05-18T01:00:46.388995Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:00:46.388995Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zODXQkhT5u1Os4/xOx6LHFahSdH6Mt8nE4HLwCjVXqOO/Z7K2za/G8Zv7cXek7ilzePzyKouJk+tMnvcU5wFDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:00:46.389461Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.7201","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e4b243e9ec190d4c8116a8424fca9cf4e0f4096914bbb9b2028917b4224376ea","sha256:972d9200fd62beae7c6ac26ad800f012688246f657a85379394c47580361b1b3"],"state_sha256":"f0fb9c268079eb2b96a72aa3b2fd670dbbfd289a51bd8da61805d91871437523"}